We recall this case here from [1]} because it illustrates the steps (ii)-(iv) of the posetification procedure very clearly. We start by defining the relation \(R_{\mathcal {P}}\subseteq \mathcal {P}\mathsf {V}X\times \mathcal {P}\mathsf {V}X\)  by
\(\hfill (a,b)\in R_{\mathcal {P}} \Leftrightarrow \exists c\in \mathcal {P}\mathsf {V}X^\mathbb {2}.\, \pi _0[c]=a \ \& \ \pi _1[c]=b\hfill \) 
